- A
- B
- C
- D
Step-by-Step Solution
The reciprocal of the reciprocal brings you back to the number, so flip again: . Check: . ✓ The trap is dropping the sign — the reciprocal of a negative number is always negative.
Answer: D)
The reciprocal of a rational number is . What is ?
Class 8Rational NumbersRational Numbers
Key idea: Identities and inverses
**Additive identity**: 0. For any rational a: a + 0 = a.
**Multiplicative identity**: 1. For any rational a: a × 1 = a.
**Additive inverse** (negation): For a, the additive inverse is −a. Their sum is 0. So a + (−a) = 0.
**Multiplicative inverse** (reciprocal): For non-zero a = p/q, the multiplicative inverse is q/p. Their product is 1. **0 has no multiplicative inverse** (1/0 is undefined).
**Multiplicative identity**: 1. For any rational a: a × 1 = a.
**Additive inverse** (negation): For a, the additive inverse is −a. Their sum is 0. So a + (−a) = 0.
**Multiplicative inverse** (reciprocal): For non-zero a = p/q, the multiplicative inverse is q/p. Their product is 1. **0 has no multiplicative inverse** (1/0 is undefined).
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More Class 8 Rational Numbers practice
How many rational numbers with denominator 63 lie strictly between 2/7 and 3/7?Between which two consecutive integers does -11/4 lie on the number line?The sum of two rational numbers is -1/3. If one of them is 5/6, find the other.Use the properties (not brute force) to compute 3/8 × (-4/5 ) + (-4/5 ) × 5/8.Which rational number is its own additive inverse?